I have some basic knowledge of iOS development and I want to now start connecting my apps to databases hosted on the internet, so that users will have access to remote / public data that pertains to my app.

My problem is that after searching the internet for some advice, I realised I don't even know what this type of programming is called? From my perusing it doesn't even appear to have a common moniker, and this is making it really difficult for me to find any advice on how to even begin learning to connect my apps to a web database.

So my questions are, what on earth is this discipline called? And, how can I get started in learning it?

Today the most common web services types are SOAP and REST. There are some iOS application that use .Net Web Services and you can create your own as per your requirement. You can use either Json or xml for getting data from database through webservice.

RestKit is a generalized framework for consuming JSON/XML over HTTP. It will interoperate with any backend, providing the payload can be expressed as key-value coding key paths.

I use SudzC webservice generator every time, it will generate a complete set of required files
and it takes you less then 5 min to get started. Dont forget to watch the video tutorial, it will explain all you need to do.